In general, will the system's sound be defined by the weakest (cable) link in the chain, in which case all the more expensive cables are a waste of money?
No. Not at all.
Or will a mix of cables that includes some really high-end ones sound better than a consistent run of the cheaper stuff?
Maybe. Probably. Sort of. Way I see it, completely beside the point.
Here is, as near as I can tell, how it works. To clue you in that I speak from experience: https://systems.audiogon.com/systems/8367
I've used everything from freebie patch cords to $4k Synergistic Research Atmosphere Level III Euphoria. I've done a budget system where the total cost was $1200 and I've put a $2k interconnect in that system. So I know what I'm talking about.
The crappiest weakest wire does not determine the sound of the whole system. BUT if you do have a crappy cheap plastic patch cord AND everything else is much better then it does make sense to upgrade the weakest link- but NOT because its better but only because its CHEAPER!
You could for example leave the patch cord in there and still get a nice improvement with an upgrade to any other piece of wire. But the wire you get would have to be better than the wire it replaces, or its a downgrade not an upgrade. Its just a lot easier and cheaper to find something better than a patch cord. So that is the one to do. Not because it is the limiting factor. There is no such thing. But simply because it is the least cost for the most improvement.
In my system for example I could get probably about the same improvement by upgrading the interconnect, speaker cable, or power cord. But a better interconnect would be $5k, better speaker cable $7k, while a better power cord would be only about $1k. Guess which one I would do first?
Yes, the power cord. But only because I have already done the fuses. What?!?! Yes the fuses. And the springs, cable elevators, room... oh wait maybe the diffuser. Keep putting off doing the diffuser.....
See, you asked about cables but the question really is how to get the best sound for the money. Right? This calls for taking a view of the whole system from like 10,000 feet. If you do that and your whole system- everything from the breaker box to the walls of your room- is so good the easiest/cheapest thing you can do is upgrade one interconnect, then by all means upgrade that interconnect.
Whether or not it is cheap or expensive. What the one you are replacing costs is nothing to do with it. My last speakers were $16k retail. The current ones $5k. But they are much, much better. That's what matters. Maybe you find something like I did costs less but sounds better. Its the sound that counts. Not what it cost. How it sounds. Got it?